THERMAL COKDUCTIVITY OF LIQUIDS
3017
Thermal Condilnctivity of Liquids
by Sheng Hsien Lin, Henry Eyring, and Walter J. Davis Department of Chemistry, University of Utah, Salt Lake City, Utah
(Received J u n e 1 , 1965)
The significant structure theory of liquids is applied to calculate the thermal conductivities of liquids. Pressure and temperature effects on thermal conductivities are discussed. For the three substances, nitrogen, argon, and methane, the discrepancy between the calculated and experimental results is less than 4y0.
I. Introduction Application of the method of significant structure theory to both thermodynamical and transport properties of liquids has been made wit’h good The purpose of this paper is to examine the thermal conductivity of liquids based on the “significant structure” model, ie. K1
=
(V,/V)K,
+ (1 - V5’V)Kg
(1)
where K I is the contribution to the liquid thermal conductivity, K , is the Contribution by the “solidlike” or lattice vibrational degrees OF freedom, and IClz is the contribution by the “gas-like” or fluidized degrees of freedoin. For the calculation of K,, we use the phonon theory first developed by Peierls4 6 and then the con-. modified by Kleniene6 and C a l l a ~ a y . Since ~ tribution of K , to the liquid thermal conductivity irr sinall, generally less than 5% except in the critical region, we use the idleal gas formulas for the calculation of K,. Three substances-argon, nitrogen, andl methane-are chosen for calculating the liquid therim I conductivity. Pressure and temperature effects on the thermal conductivity are also discussed.
11. Thermal Conductivity of Solids When a temperature gradient is applied to a solid, the equilibrium state will be disturbed, and the average distribution of phonons should be determined from the Boltzmann equation - C,
grad T d N / d T
=
blV/bt
(2)
where N is the number of phonons per unit volume and C, the group velocity of solids. The left-hand side of eq. 2 represents the rate of change of N due to the transport of phonons, and this is balanced by the rate
of change due to scattering processes indicated on the right-hand side. Since the exact solution of eq. 2 is i~npossible,~ an approximation is made by putting6
N=Nfl+n (3) Where N Q is the equilibrium distribution, Nfl = - l)-‘. It is apparent that if the temperature gradient is small, then n < lO-*O, B = 5.64 X and A = 1.60 X B == 1.77 X respectively. Below the critical ternperatures, the liquid thermal conductivity is nearly a linear function of temperature at constant pressure as shown in Fig. 1 and 2. To consider the pressure effects on the liquid thermal conductivity, we USE C, = ( y , / p , / ? ~ ) ~ ”to estimate the dependence of C, on the pressure, where y, is the ratio of specific heats of solids, p,, the density of solids, and PT, the isothermal compressibility coefficient of solids. C, does not vary very much with pressure, so we have to consider the pressure dependence of C, only a t very high pressures. Because of being limited by the availability of data for @I, only two values of Kl under the pressure of 8 0 0 K , / c n ~have ~ been calculated for argon. The data used for the calculation are P = 0, PT = 6.2
4,00r
80
120 T
I60 OK
Figure 2. Temperature dependence of Kl of nitrogen: , experimental values; A, calculated values; curve 1, P = 33.5 a t m . ; curve 2, P = 134 atm.
X ~ n i . ~ / K and , , P = 8 0 0 K , / ~ m . ~PT, = 4.36 x 10-j c n ~ . ~ / K , .V~ ~= 28.89 ~ i n . ~ / m o laet T = 119.6 OK.; V = 27.54 ~ r n . ~ / m o l at e l ~T = 102.2 OK. The results obtained by using eq. 17 are K 1 = 3.30 X cal./deg. cni. at P = 8 0 0 K , / ~ n i . ~T, = 119.6OI
